Finite Group DatabasebetaFinite Group Databasebeta| order | 7424 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C29 · Schur multiplier (H2) = C22×C4 |
| direct product | C29×#8239 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×C22⋊C4 |
| commutator | C2×C4 | C2×C42×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| socle | C22×C29 | C4×C22⋊C4 |
| prime radical | C29×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C8×C29 ◁ G | |
510 conjugacy classes of subgroups.
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7424, 1227);